Slope stability analysis is a multi-scale problem. Typically, owing to the distinctions of slope scales (e.g., slope height or slope angle) in practical engineering, the stability calculation results of slopes with various scales from numerical methods inevitably exhibit different computational precision levels in the case of identical computational grids, and therefore the stability results of different slopes cannot be compared. To achieve equal accuracy stability analysis for multi-scale slopes, this study establishes numerical models of slopes with various scales as well as different grid shapes and sizes to conduct stability analysis. The results show the following: (a) a positive correlation relationship exists between the safety factor of the slope and the scaling factor, which is defined as the ratio of the grid size to the slope height; (b) the definition of the refined safety factor is given, representing the safety factor that corresponds to the infinitesimal grid size and eliminating the computational error of slope stability analysis caused by grid size or shape; (c) on this basis, embarking on the composite influence of multiple scales of slope on stability analysis, the study proposes a simplified treatment method suitable for evaluating the refined safety factor of the multi-scale slopes, which is verified as valid and feasible by some examples.

中文翻译：

---

多尺度边坡稳定性分析的精确评价方法

边坡稳定性分析是一个多尺度问题。通常，由于实际工程中坡度尺度（如坡高或坡角）的差异，数值方法对不同尺度的边坡稳定性计算结果，在计算网格相同的情况下，不可避免地表现出不同的计算精度水平，因此不同坡度的稳定性结果无法比较。为实现多尺度边坡等精度稳定性分析，本研究建立了不同尺度、不同网格形状和尺寸的边坡数值模型进行稳定性分析。结果表明： (a) 边坡安全系数与比例因子(定义为网格尺寸与坡高的比值)之间存在正相关关系；(b) 给出了细化安全系数的定义，表示对应于极小网格尺寸的安全系数，消除了网格尺寸或形状引起的边坡稳定性分析计算误差；(c) 在此基础上，研究多尺度边坡对稳定性分析的复合影响，提出了一种适用于评价多尺度边坡细化安全系数的简化处理方法，经验证其有效性和可行性一些例子。